December 12th, 2009, 06:40 AM  #1 
Member Joined: Oct 2009 Posts: 85 Thanks: 0  Ring Homo. 1) show f not a ring homo. over 2) show f is a ring homo. over for part 2) we have . Then . So we have and . Is this all that has to be shown for 2? And for part one I dont know how to go about not showing homo. 
December 12th, 2009, 11:55 AM  #2 
Senior Member Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0  Re: Ring Homo.
For part 1, just show any counterexample to f(x + y) = f(x) + f(y) or f(xy) = f(x)f(y). I recommend the additive portion  every counterexample I can think of for the multiplicative portion exploits the problems of the additive one.


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